44 Mag minimum! With real bullets, solid hard casts, like Ripp said. Mine is loaded with Keith style cast from wheel weight alloy with heat treat. No fast expanding jacketed bullets.

Figure out in advance where to shoot 'ol bruin, cause if he is coming at you, a head shot may not work, I would go for the spine. Up the nose if you are good. Practice shooting eggs at 50 feet, one handed, you may not have time enough for a two hander. I was charged by a big black when backpacking, lucky for me he turned at about 20 feet and ran off. From the moment I first saw him until he turned there was not enough time for me to pull the M629 out of the holster. Good thing it was not a Griz or a Brown! If I was in serious griz/brown country, the 629 would be in a quick access front holster.

Check state regs, some do not allow a firearm to be packed when bowhunting.